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Related Concept Videos

Convolution: Math, Graphics, and Discrete Signals01:24

Convolution: Math, Graphics, and Discrete Signals

In any LTI (Linear Time-Invariant) system, the convolution of two signals is denoted using a convolution operator, assuming all initial conditions are zero. The convolution integral can be divided into two parts: the zero-input or natural response and the zero-state or forced response, with t0 indicating the initial time.
To simplify the convolution integral, it is assumed that both the input signal and impulse response are zero for negative time values. The graphical convolution process...
Convolution Properties I01:20

Convolution Properties I

Convolution computations can be simplified by utilizing their inherent properties.
The commutative property reveals that the input and the impulse response of an LTI (Linear Time-Invariant) system can be interchanged without affecting the output:
Convolution Properties II01:17

Convolution Properties II

The important convolution properties include width, area, differentiation, and integration properties.
The width property indicates that if the durations of input signals are T1 and T2, then the width of the output response equals the sum of both durations, irrespective of the shapes of the two functions. For instance, convolving two rectangular pulses with durations of 2 seconds and 1 second results in a function with a width of 3 seconds.
The area property asserts that the area under the...
Deconvolution01:20

Deconvolution

Deconvolution, also known as inverse filtering, is the process of extracting the impulse response from known input and output signals. This technique is vital in scenarios where the system's characteristics are unknown, and they must be inferred from the observable signals.
Deconvolution involves several mathematical techniques to derive the impulse response. One common approach is polynomial division. In this method, the input and output sequences are treated as coefficients of...
Transformations of Functions III01:20

Transformations of Functions III

Transformations modify the graphical representation of a function without changing its fundamental form. One common transformation is reflection, which flips the graph across a designated axis. When the vertical coordinates of all points are multiplied by the negative one, the entire graph is mirrored over the horizontal axis. This transformation reverses the vertical orientation of peaks and troughs, akin to signal inversion in electrical systems, where a waveform is flipped, but the timing of...

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Related Experiment Video

Updated: Jul 7, 2026

Quantitative Optical Microscopy: Measurement of Cellular Biophysical Features with a Standard Optical Microscope
14:09

Quantitative Optical Microscopy: Measurement of Cellular Biophysical Features with a Standard Optical Microscope

Published on: April 7, 2014

L/M-fold image resizing in block-DCT domain using symmetric convolution.

HyunWook Park1, YoungSeo Park, Seung-Kyun Oh

  • 1Department of Electrical Engineering, Korea Advanced Institute of Science and Technology, Daejeon 305-701, Korea. hwpark@athena.kaist.ac.kr

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
|February 2, 2008
PubMed
Summary

This study introduces a fast method for resizing compressed images directly within the discrete cosine transform (DCT) domain. The novel approach offers computational efficiency and high-quality results for digital image resizing.

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Quantifying Intermembrane Distances with Serial Image Dilations
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Quantifying Intermembrane Distances with Serial Image Dilations

Published on: September 28, 2018

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Quantifying Intermembrane Distances with Serial Image Dilations
07:45

Quantifying Intermembrane Distances with Serial Image Dilations

Published on: September 28, 2018

Area of Science:

  • Digital Image Processing
  • Computer Vision
  • Signal Processing

Background:

  • Digital images are often compressed for storage and transmission.
  • Resizing compressed images typically involves decompression and recompression, which is computationally intensive.
  • Existing methods for resizing compressed images in the spatial domain are generally slower than in the compressed domain.

Purpose of the Study:

  • To propose a novel and efficient method for resizing digital images in the discrete cosine transform (DCT) domain.
  • To leverage the multiplication-convolution property of DCT for faster image resizing.
  • To achieve high-quality image resizing with minimal computational overhead.

Main Methods:

  • The proposed approach resizes images within the discrete cosine transform (DCT) domain.
  • It utilizes the multiplication-convolution property of DCT, where spatial domain multiplication corresponds to symmetric convolution in the DCT domain.
  • The method operates on 8x8 block-DCT coefficients, producing resized images also in 8x8 block-DCT coefficients.

Main Results:

  • The proposed DCT-domain resizing method is computationally fast.
  • It produces visually pleasing images with high Peak Signal-to-Noise Ratio (PSNR).
  • The approach maintains image quality while significantly reducing processing time compared to spatial domain methods.

Conclusions:

  • Resizing images in the DCT domain is a viable and efficient alternative to spatial domain methods.
  • The novel approach offers a significant speed advantage for image resizing tasks.
  • The method is suitable for applications requiring fast and high-quality image manipulation of compressed images.